Hw5 P-7.15

# Hw5 P-7.15 - Problem 7.15 in SPF EEL 3135 Signals and...

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Problem 7.15 in SPF EEL 3135: Signals and Systems G. Heitman Electrical and Computer Engineering University of Florida Spring 2006 fs 1000 := Ts 1 fs := gcd 750 2000 , ( ) 250 = Hence the fundamental freq. and period of the C-T signal are f0 125 3 := T0 1 f0 := T0 0.024 = The input contains dc and the 3 rd and 8 th harmonics x ct t ( ) 4 cos 2 π 3f0 () t π 4 + 3 cos 2 π 8f0 t := The given C-T input x dt n x ct nTs := The ideally sampled signal. Its fundamental period is N0 T0 Ts := N0 24 = Fortunately the problem is set up so that T0/Ts is an integer The fundamental freq. of the D-T input: ω 0 2 π N0 := ω 0 1 12 π The D-T signal contains dc and the 3 rd and 8 th harmonics: 3 ω 0 1 4 π 8 ω 0 2 3 π tmin 0 := tmax 2 T0 := ε tmax tmin 1000 := t tmin tmin ε + , tmax .. := n0 2 N 0 .. := EEL 3135 1 P-7.15.mcd

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0 0.01 0.02 0.03 0.04 0.05 5 10 The C-T Input and Its Samples 4 x ct t () x ct nTs T0 tnT s , 01 02 03 04 05 0 5 10 The D-T Input 4 x dt n N0 n The D-T system function: H z 1 3 1z 1 + z 2 + := The D-T output signal: y dt n ( ) 4 H exp i 0 H exp i 3 ⋅ω 0 cos 3 ω 0 n π 4 arg H exp i 3 0 + + 3 ( ) H exp i 8 0 cos 8 ω 0 n arg H exp i 8
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Hw5 P-7.15 - Problem 7.15 in SPF EEL 3135 Signals and...

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